help-26

[arctic sundial]

Video link?

[agile harness]

they could better explain it in a video

i got you hold on

[arctic sundial]

Professor Sucks cancelled class on Monday and threw us 2 new Chapters to cover on our own

[agile harness]

https://youtu.be/_FSXJmESFmQ?si=ILJ6wYH0GOBtSU6v

[arctic sundial]

Mind you it takes 2 days for us to cover one

[agile harness]

just go down the rabbit hole of these videos

[arctic sundial]

Wdym

[agile harness]

like watch a bunch of these

you’ll get the hang of it

[arctic sundial]

Bet that up lil bro

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[sly abyss]

Help

[sly abyss]

Close

[wooden osprey]

what is your question

[sly abyss]

I wanted help in understanding this logic problem

[wooden osprey]

...

[sweet shard]

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[deft holly]

i got a as 4

from this, is there an easy way to find part b?

?

hello??

<@&286206848099549185>

[deft holly]

so <@&268886789983436800> , trolled again

[crude trail]

lol

[deft holly]

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[sonic belfry]

what is arctan(1)

[unique quarry]

pi/4

[sonic belfry]

tan(1) = sin(1)/cos(1)

so arctan(1) = cos(1)/sin(1)???

[sudden temple]

no

[sonic belfry]

😭

[unique quarry]

cos = 1 and sin = 1

[dry zenith]

That's not the definition of arctan

[sonic belfry]

oh

[lusty marsh]

nope

[dry zenith]

that's the definition of cot(x)

[wooden osprey]

lmao

[dry zenith]

tan(x) = sin(x)/cos(x)
cot(x) = cos(x)/sin(x)

[sonic belfry]

oh

wait

then whats arctan

inverse tan

what does that mean

1/tan(x)

[wooden osprey]

probably they thought $\tan = \frac1{tan^{-1}}$

[wooden osprey]

if $\tan x= a$, then $\arctan a = x$

[sonic belfry]

oh

[wooden osprey]

no that is not true

[sonic belfry]

oh right-

[wooden osprey]

in more technical terms, arctan is the inverse function of tan, just like you said

[sonic belfry]

arctan(1) = tan(u) where u = something that would make tan(u) = 1????

[sudden temple]

arctan(1) = u is what you probably meant

[sonic belfry]

and how would you know that the answer is pi/4

[merry hill]

impose tan on both sides

1 = tan(u)

and where is tan(x) = 1? pi/4

[sonic belfry]

ok thanks also how do i make my calculator not give the answers in degrees

and radians(i think) instead

[dry zenith]

What's your calculator's type/model?

[sonic belfry]

ti30x

[dry zenith]

There should be a settings menu about it

I'm guessing angles or something

[sonic belfry]

oh i see

thanks

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[sinful harness]

Can someone help me find pb

[sinful harness]

helloooooo\

[supple hinge]

hi

i"ll try

are ap and ac bisectors or smthing like that

ap and cp**

[sinful harness]

tbh im not really sure how to start this problem

the question is like this

let P be a point inside rectangle abcd. if pd = 12, pc = 7, pa = 10, find pb

[supple hinge]

i think u should use trignometry

[odd forge]

https://brilliant.org/wiki/british-flag-theorem/ @sinful harness

I think this it it

[supple hinge]

use the British flag theorem, which states that for any point inside a rectangle, the sum of the squares of the distances from that point to two opposite corners is equal to the sum of the squares of the distances to the other two opposite corners. the formula is like this PA^2 +PC^2 = pb^2 +Pd^2

i was typin that

[odd forge]

yea

with proof

[supple hinge]

@sinful harness

did u understand

[sinful harness]

ohhhh wait ill try to understand let me see ill studyyy it thank youuuuu so much

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[hushed cliff]

Can someone help me solve this question ?

[silk delta]

hold up gimme one minute

[hushed cliff]

ok thanks

[silk delta]

is PR the radius tho

not given?

[hushed cliff]

no

[silk delta]

alr cool

so

We can find angle PSR first

[hushed cliff]

is it 90?

[silk delta]

by using the fact that the opposite andles of cyclic quadrilaterals are supplementary

[silk delta]

I get what you mean, but since PR isn't the radius it isn't 90

[hushed cliff]

oww ok

[silk delta]

hmm wait you're Malaysian aren't you

[hushed cliff]

ya

[silk delta]

so you got the answer?

[hushed cliff]

98?

[silk delta]

yep

then we can find angle PST

[hushed cliff]

PST=39

is the 74 include qpr?

[silk delta]

hmm yeah seems like the 74 degrees is QPS

[hushed cliff]

ok then i got it

thanks for your help

[silk delta]

np

[hushed cliff]

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[dire mural]

Another weird one

There is a c part but that part is just pure word choice

oh way lemme fix b part

[neon iron]

What have you done till now?

[dire mural]

f>0 or f<0 in (0;1)

so f(x)>2024|f'(x)|

or f(x)<-2024|f'(x)|

[opal vault]

have you shown part a then?

or

[dire mural]

part a?

[opal vault]

is this done

[dire mural]

nah not yet

i'm trying to prove f(x)>2024|f'(x)| wrong

if that is wrong

then part a is done

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[jolly urchin]

https://media.discordapp.net/attachments/1181271232864337950/1293604079582449664/Screenshot_20241009-1800002.png?ex=6707fa2e&is=6706a8ae&hm=d258ae912b17cd43fe17d9f810b1be9372e5216affefcea84a2da18310bb330d&

[jolly urchin]

Could someone explain

[neon iron]

caught the translation uptil here

do you know what natural numbers are?

[jolly urchin]

Yep!

[neon iron]

nice

[jolly urchin]

Positive integers

[neon iron]

they are represented by the Alphabet N

similarly we are now introducing a new set of numbers called rational numbers

they are denoted by Q

they are defining(saying saying that)Q as any number which can be written of the form p / q

$p/q$

[thorny flame]

Cnidarian

[neon iron]

where p can be any integer

and q is any integer except 0

this is what they meant over here

q not equals 0

they are also saying that all rational numbers can be added,subtracted,multiplied and divided

[jolly urchin]

I See! Thank you a lot!

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[rocky sky]

Can someone explain to me why at step 3 we dont just get rid of the +9/16 and -9/16?

so that it would become 2(y^2-3/2y)

[cunning kayak]

to make it a perfect square

[rocky sky]

i still dont understand, normally with a completing a square we add the number outside the brackets?

[cunning kayak]

process to make a perfect square

this will help you understand better

[rocky sky]

Thanks, ill look into it

what if one doesnt have a c value?

[cunning kayak]

c=0

[rocky sky]

ohh its just invisible so to say

[cunning kayak]

yeah

[rocky sky]

is it possible to use completing the square to simplify an expression?

such that we try find out what x is equal to?

[cunning kayak]

yeah

we can use it for finding factors

[rocky sky]

i figured id use that sheet and try again from the start of one of my lines.
4x^2-x+0

4(x^2-1/4x+0/4

but its known that 0 cannot be divided with, right?

so instead would we try
4(x^2-1/4x)

[cunning kayak]

0/4 = 0
4/0 = undefined

[rocky sky]

oh...

[cunning kayak]

yeah so here 0/4 would become 0

[rocky sky]

so it would then turn into 4(x-1/8x+0)

[cunning kayak]

here u wrote 1/4

[cunning kayak]

and here 1/8

whats the ques?

[rocky sky]

ill get it up

[cunning kayak]

4x^2 - x?

[rocky sky]

5X 2 −3X+4Y 2+2XY−6Y+7X 2
To simplify

12x^2-3x +4y^2 -6y +2xy

3(4x^2-x) +2(2y^2-3y) +2xy

To solve first part of x we should take

4x^2-x+0
4(x^2-1/4x+0)

4(x^2-1/8x+0)
4(x-1/8x+0 -1/64)

I added 0 in as the placeholder for c in the previous picture

[cunning kayak]

5X^2 −3X+4Y^2+2XY−6Y+7X^2

?

[rocky sky]

Yes

sorry i forgot to put ^ after 4y

and the 5x

[rocky sky]

but this is in the question and it is asking us to simplify completely

[cunning kayak]

is it 7x^2?

[rocky sky]

yes

[cunning kayak]

it wont get simplified more

i guess

[rocky sky]

huh

could we not factorise to simplify?

[cunning kayak]

try if you can

but i think it will make it more complicated

[rocky sky]

ok

ill try and do it lol

4x^2-x

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[rocky sky]

4(x^2-x+0)
when attempting to complete the square

turns into something like 4(x-1/8x+0-1/64)?

<@&286206848099549185>

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[willow nest]

hp

[willow nest]

how to start proving from the left side

[willow nest]

ermmmmmmmmmmm

nothing

except that cos2theta is cos^2a-sin^2A

,rotate

[willow nest]

[agile harness]

are you sure about the sin3x

[willow nest]

no

im not

i forgor

how to simplyify that

[agile harness]

use angle sum then

sin(2x+x)

expand

sin2xcosx + cos2xsinx

then expand the double angle

[willow nest]

oh valid

ok wait

chat

its not working ot

,rotate

[willow nest]

heklp

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[wintry crater]

what did i do wrong here?

[wintry crater]

<@&286206848099549185>

[sweet shard]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[cloud mango]

,w sin 30

[thorny flame]

Results provided by WolframAlpha

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Requested by ayy_m_d

[cloud mango]

yeah i mean i'm failing to see the error here

[tacit osprey]

both questions are different right

[cosmic silo]

it is quite right

[wintry crater]

the first pic is the problem, the second pic is my work

the online software's marking wrong idk why

[tacit osprey]

Your solution seems right

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@wintry crater Has your question been resolved?

[wintry crater]

<@&286206848099549185>

[tacit osprey]

Bro your answer is correct

[toxic otter]

[tacit osprey]

I even read vectors again to rechecked it

[wintry crater]

would you say there's something wrong with the software?

[toxic otter]

let me check

it is correct

the engine is shitty

[wintry crater]

ok

the computer said this is the correct answer:

how??

[wintry crater]

<@&286206848099549185>

[tacit osprey]

Shit your system is shit

[wintry crater]

pls help me why the computer favors 2√27 over 6√3

[tacit osprey]

If you take the root of 27 if will be 3√3 and multiply it with 2

[wintry crater]

oh so they're equivalent?

[tacit osprey]

Nothing will happen your answer is correct

[tacit osprey]

Yrs

[wintry crater]

this made me laugh

thanks haha

[tacit osprey]

No problem

[wintry crater]

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[quasi prairie]

can someone pls help me with this question

I'm struggling

<@&286206848099549185>

[neon iron]

which one

can you type it pls cause im blind without my glasses

nvm

which question

[quasi prairie]

uh everything from b onwards

i got a

[neon iron]

for b
it is a geometric series with a constant ratio of 1.02 (from the 2% interest). You can apply the geometric series formula to prove the total value of Phil’s savings after 20 years.

for c use the equation from part b and solve for P by equating the total value of his savings to the amount he owes after 20 years.

d.i use present value formula for an annuity

d.ii use perpetuity formula

these are hints btw not answers

[quasi prairie]

thank you!! i prefer hints so that's really helpful

[quasi prairie]

what is the perpetuity formula?

[neon iron]

Present Value (PV) = Cash Flow (CF)/Interest Rate (IR).

[quasi prairie]

oh, I haven't learnt about cash flow

but this question was in my test

[neon iron]

ig its extra knowledge

[quasi prairie]

is that the only way to solve d?

[neon iron]

maybe

didn't look at it that intently tho

di or dii

[quasi prairie]

Wdym

you mentioned that i should use the perpetuity formula to solve dii

and the present value formula for di

[neon iron]

oh yeah

sorry

[neon iron]

probably not but its the simplest way to do so

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[honest musk]

How would I go on about turning this into standard form? (Nvm, I think I got it)

[honest musk]

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[high quail]

(lemme see if I just forgot the bases

[alpine mist]

the x^2 should be in the same log as the y and z terms

log(A) + log(B) = log(AB)

and yes, it should be log_7

[high quail]

like this?

[alpine mist]

oh, you also need to distribute the 2

[high quail]

Wdym

[alpine mist]

that 2 in front is multiplied onto everything. not just the first log

[high quail]

ohhhh

[high quail]

so would it just be x? and 2 next to the log

[alpine mist]

no, you need to distribute it, and then use the power rules, and sum/difference rules
or use the power rule at the end.

[high quail]

ohh

[high quail]

There we go it worked, Thanks!

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[neon iron]

How do you find an equation for 3.) a.) ?

Is it not 2x(16-x^2)?

What is this question talking about

[cedar sinew]

Wait why 2x

Why not just x

Explain your Reasoning

Oh I See

The area of a rectangle is base times height

It seems to me that you wrote 2 times base times height

Remember

Rectangle is base times height

And triangle is half base times height

Very Imporant Theorem

@neon iron do you understand?

It’s a little complicated

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[vernal dawn]

So I have to find the derivative using the chain rule

So from my understanding for exponents

Its supposed to be (e^tsin2t) * g'(x)

So when I did the work, I got (e^tsin2t) * (tcos2t)

But the textbook answer shows this:

I'm just curious as to what I did wrong here

Since the derivative of sin should just be cos

[neon iron]

Pls help

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[vernal dawn]

Lemme check the textbook

I didn't see a product rule being mentioned

Yeah theres no mention of a product rule

And the prof didn't mention it

Yeah I went back to doublecheck to make sure.

Maybe I missed it because I was braindead from all the exams.

I'll ask them tomorrow and come back later.

Thank you.

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[proven narwhal]

Not sure where I messed up

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[proven narwhal]

<@&286206848099549185>

[proven narwhal]

<@&286206848099549185>

[proven narwhal]

<@&286206848099549185>

[rocky flower]

Yeah

[proven narwhal]

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[tranquil birch]

Heeeelp with this again

[gray ridge]

!status

[topaz sinew]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[tranquil birch]

1

lol

[gray ridge]

Hint 1: area of APD + area of PBC = half the area of the paralleogram ABCD

[tranquil birch]

can i prove it?

[gray ridge]

sure

draw a line BD, compaer
area of APD + area of PBC
and
area of ABD

e.g. they are of same height with base on AB

[tranquil birch]

ooh i see

[gray ridge]

Hint 2: area of QBC is half of the area of parallelogram ABCD

[tranquil birch]

oooh so APD +PBC=QBC? and QBC=QPB +PCB?

[tranquil birch]

it would be all But how i can prove this ?

[gray ridge]

same base length, same height

just that one is parallelogram, one is triangle

[tranquil birch]

oh nicee i get this

[gray ridge]

great!

hope all that helps!

[tranquil birch]

thank you so much

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[neon iron]

I’m supposed to find the slope of the graph at (3,1). In another problem I did previously, I differentiated every term with respect to x, and then I isolated dy/dx terms to solve. However, I’m very stuck on the calculus portion and I’m confused on how to further differentiate this equation.

[static viper]

,rotate

[static viper]

Everything you have done is fine so far

[fading owl]

Implicit differentiation?

[neon iron]

Yes

[static viper]

Which term do you have trouble differentiating?

[neon iron]

D/dx[(x^2 + y^2)^2]

Do I have to use the chain rule for this term?

[static viper]

Yup

[fading owl]

Yea

[neon iron]

Would I represent (x^2 +y^2) as one variable or would it be as a function of x

[static viper]

Function of x

[fading owl]

The latter i think

[neon iron]

So it would be u(x)= x^2 + y^2

[static viper]

It's similar to (sin x) ^2

[fading owl]

Uh yes

[neon iron]

And then y(u)= u^2

Ok

[static viper]

What?

Uh sure

Yea

[neon iron]

Does this look right?

The last line

[static viper]

Yup

[neon iron]

Wait but I already did the chain rule once before

Second line

[static viper]

Doesn't matter

[neon iron]

I just keep on doing it?

I’m confused

Every time I use the chain rule on that term it’s just giving me the same term

I keep getting d/dx[(x^2 + y^2)^2] and d/dx[x^2+y^2]

Would it be correct if I wrote that d/dx[(x^2+y^2)^2] is equal to 2(x^2+y^2) because of the power rule

[static viper]

This is correct

[static viper]

Sorry this was wrong didn't notice it wouldn't be whole square and it wouldnt be the derivative

2(X^2 + Y^2) * d/dx(x^2 + y^2)

[neon iron]

Okay

So now I’m stuck on how to isolate dy/dx

[static viper]

Can you send where you are stuck

[neon iron]

Last line

[static viper]

You'll have to multiply but before that take 2 common and cancel with 100

[neon iron]

I can take 2 out of dy/dx[2y] ?

[static viper]

Yup

[neon iron]

Ok

How do I cancel with 100?

Should I divide both sides by 6?

[static viper]

By 4

[neon iron]

So leave the coefficient of 3 alone then?

[static viper]

Yup

[neon iron]

Ok

I will distribute and try to isolate now

Nevermind I will not the polynomials are too big

[static viper]

Or

[neon iron]

I am confused how to get dy/dx out since there are added terms in the parentheses

[static viper]

You could put x = 1 and y = 3

[neon iron]

True

Actually not yet

I still have to solve for the derivative

[static viper]

It wouldn't be that hard to distribute

[sterile finch]

,rotate

[static viper]

You'll be able to take dy/dx common between two terms

[neon iron]

Ok let me try that

[sterile finch]

,rotate

[neon iron]

This looks really weird I don’t know if I did it right

[sterile finch]

dy/dx(y^2) on the second to last line should by dy/dx (y^3)

,rotate

[neon iron]

Correct, my bad

I think I did something wrong in the last few lines

I used a calculator to get this answer

[sterile finch]

,wolf f(x,y) = -(3xy^2 - 25y + 3x^3)/(3y^3 + 3x^2y - 25x) for (x,y)=(3,1)

[thorny flame]

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[quasi prairie]

How do they take it as an arithmetic sequence without any mention of it being one?

[night imp]

Can you see the pattern?

123 then 130 then 137...

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[strong sable]

what does this come from? It looks like dot product but how can we turn g(x,y) into a dot product form like this?

[loud oasis]

in this situation $\langle a, b \rangle$ just denotes a vector with components $a$ and $b$, similar to $(a,b)$ or $\begin{pmatrix} a \ b \end{pmatrix}$

[thorny flame]

cloud

[strong sable]

then how did they decompose g into a vector like that?

[thick lily]

it's the gradient of g

it's that formula on the left there

[strong sable]

lmao yes im being stupid

tysm

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[thick lily]

yup yw

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@strong sable Has your question been resolved?

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@strong sable Has your question been resolved?

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@strong sable Has your question been resolved?

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[merry hill]

what

[neon iron]

i don't know, that's why i asked.

[merry hill]

is that mcc

if it is, what is m

[flint stump]

can you type it? Does it say 5*pi/9 + 5*pi/18 (in radians?) + mcc(?) = pi?

[chilly walrus]

i think it's m (for measure) of angle c

[neon iron]

measurement of angle C

[flint stump]

Ahh, alr

[neon iron]

and the is s = 5

[flint stump]

then it is just simple subtraction, after you move all the known angles on one side

[neon iron]

ok

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[fiery bluff]

Hello guys, have a question about solution of this problem, recently found some explanation from one of the helpers towards my classmate, but I couldn't get to solution after reading and understanding of this explanation (will send it after this massage)

[topaz sinew]

@fiery bluff Has your question been resolved?

[fiery bluff]

<@&286206848099549185>

[fiery bluff]

<@&286206848099549185>

[orchid citrus]

hi

[fiery bluff]

Hi

[fiery bluff]

R u still here ?

🥲

[charred moat]

okay

[charred moat]

I can't see a thing, zoom it in or type the question please

[fiery bluff]

W8, which one u cant see?

The assignment or?

[fiery bluff]

?

[charred moat]

assignnment

[fiery bluff]

Ok, give a sec, will send it as a text

[fiery bluff]

We have a rectangle with dimensions of m x n meters, on the surface of which there is a satellite at the initial position with coordinates (x, y) (where the initial position is not on any of the sides of the rectangle). It can move around the inside of the rectangle and bounce off its walls (see picture). Assume that the satellite has negligible dimensions and consider the angle a V in the range 0 < a < 360°

1. We have specified the maximum distance D that the satellite can cover. As a function of D, determine how many different pairs (d,a) exist, where d < D denotes the distance traveled by the satellite at the angle at which it begins to move, such that the satellite stops at exactly one of the corners of the rectangle?
2. We have specified the maximum number of reflections of the satellite N. Let us calculate that the reflection by the corner of the rectangle is counted as two reflections. How many different pairs (n,a) exist, where n < N denotes the number of reflections of the satellite on the edge of the rectangle and and the angle at which it starts to move, such that the satellite stops exactly at the corner of the rectangle after exactly n reflections?

As can be seen in the image below. if we have a 3 x 3 kilometer square, starting position as in the picture and allowing at most one bounce, there are 12 different solutions. The answer in this case is V, so 12.
This task is purely theoretical, in addition to the correctness of the solution, pay attention to the procedure and justification, why your procedure is correct - why the model can be described in a certain way, why some property or algebraic modification applies, etc. Without a proper explanation of the important non-trivial steps, you will not be awarded full points.

Since this assignment in not basically written in English but was translated by me from Czech, just in case something not gonna make sense feel free to ask I will translate it separately

And yeah r u still here ?

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[fiery bluff]

<@&286206848099549185>

That's not funny 😢

[fiery bluff]

<@&286206848099549185>

[fiery bluff]

<@&286206848099549185>

[dry zenith]

Please don't ping helpers multiple time, It's a good idea to ask in one of the advanced channels too I think

[fiery bluff]

Okey sorry, just followed instructions that was given to me by bot, can u recommend some please?

[dry zenith]

I think #geometry-and-trigonometry might be fitting here

[fiery bluff]

Thanks, will ask there, appreciate it

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[neon iron]

there is no progress WHATSOEVER

[mortal steeple]

Draw diagram and send

[neon iron]

okay

this should be visible

any direct aproach is not helping

Angle bisector theorem

what is its statement?

you can search on YouTube if you dont know how to use it

its best to learn early

[limber prairie]

,w angle bisector theorem

[thorny flame]

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[mortal steeple]

https://images.app.goo.gl/PpnZtYFdJqKUv57Z8

Here lol

[neon iron]

yes

[mortal steeple]

a/b = x/y

@neon iron ?

[mellow breach]

we have to find angle>

[mortal steeple]

jee thanks didn't realise

[neon iron]

I have formed two equations.

I just need to find positive solutions for them

[mortal steeple]

Linear equations?

[neon iron]

Here are those:

sin(2A+B)/(sin(B)) = 2cosA
3A + 2B = pi

[mortal steeple]

Hmm

Send your calculations

[neon iron]

I am not sure I will do that rn

[mortal steeple]

.

You are in 9th right?

[neon iron]

yes

[mortal steeple]

You can't use trig lol

[neon iron]

well these questions won't be asked in my exam

[mortal steeple]

Send you calculations

[neon iron]

the third case only gives positive values of A and B both

which is 0.2 pi and 0.2 pi, this implies A = B

now I think I am done

[mortal steeple]

Okk

[neon iron]

which gives our answer as 72 deg / 9 = 8

how fun

i didn't know geometry can be this non-ambiguous

That angle bisector theorem helped me

thanks

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[mortal steeple]

She used some AI lol

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[neon iron]

wolfram alpha

[neon iron]

shi*

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[livid fox]

I need help solving week 5 and 6 of this time series table using 0.2 to find smoothing values

[sweet shard]

show the rest of the problem. nobody but you knows what alpha is supposed to be

[livid fox]

The whole problem

[sweet shard]

show the formula with exp. smoothing parameter you were taught

[sweet shard]

wut

that's just a table of numbers

[livid fox]

The formula is up top

[sweet shard]

can you just type it here

[sweet shard]

how did you get 15.38

[sweet shard]

seems like you already know how to calculate it since you got the first few weeks right

[livid fox]

Yea but what I think is the right answer isn’t right

[sweet shard]

how did you get 15.38

show the exact calculation you made

[livid fox]

15.38 is just a guess, I’m just trying to put different numbers in there at this point. I’m on submission 5/10 and it’s still not working

[sweet shard]

how did you get the previous 3 values correct then

[livid fox]

I did it by myself but I messed up the table trying to figure out how to do week 5 and 6

Chatgpt getting it wrong too

Formula I used is up top

[sweet shard]

don't use chatgpt for math

type your formula here

[livid fox]

I know I was just lost

=$K$21*E27+(1-$K$21)*F27

[thorny flame]

PotatoCaleb

[sweet shard]

wut

this is a formula

[livid fox]

Brb

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@livid fox Has your question been resolved?

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[mortal patrol]

I have a question again about fourier series. It's about calculating the sum of an even function

[mortal patrol]

And I have a given fourier series

The function is even

This is the given fourier series

Now the question is to calculate the sum of this fourier series for t=0 and t=2

My first question, how do I confirm if the function is discontinous at t=0 or t=2?

[sweet shard]

why do you think f(t) is disctoninuous at t=0?

[mortal patrol]

I mean it seems like it's not connected with the other part

0 at t=0

and -t + 2 between 0 and 2

[sweet shard]

oh right

[mortal patrol]

Is that the simple answer?

Or is there more to it?

[sweet shard]

indeed it is

[mortal patrol]

So for t=2

[sweet shard]

for t=0

[mortal patrol]

It's continous?

[sweet shard]

t=2 looks continuous

[mortal patrol]

okay, now the question is

How do I calculate the sum of the fourier series

for t=0

and t=2

do I just do it manually, plug in t=0 in the fourier formula and t=2?

and add them together?

[sweet shard]

why are you adding f(0) + f(2)

[mortal patrol]

I'm realizing that the question is not asking for that

So I need to calculate each seperately

[sweet shard]

,w sum k=1 to inf (1-cos(2k))/k^2

[thorny flame]

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[sweet shard]

pain

i doubt you're supposed to actually find the exact fourier series value at t=0 and 2

,w sum k=1 to inf (1-cos(2k)) * cos(2k) /k^2

[thorny flame]

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[sweet shard]

maybe t=2

[mortal patrol]

What do you suggest I do?

[sweet shard]

show the original question

[mortal patrol]

It's in a different language

hence why I translate it

But it says

''Determine the sum of the series for t=0, and t=2''

[sweet shard]

you just use this

[mortal patrol]

What do I do with it?

[sweet shard]

f(0) = 0

also equals f(0) here

[thick lily]

wait a sec, the second line says -t+2 if 0<=t as well

[sweet shard]

pain

f(t) is ill-defined

[thick lily]

isn't there a theorem that the series converges to the average of the discontinuities

[mortal patrol]

That's what I was about to ask

[thick lily]

so thinking it'd be 1

[mortal patrol]

If there is something we need to consider due to it being discontinous?

[sweet shard]

how do you find the average value of an ill-defined function

or does it not matter that f(0) is both 0 and 2

[mortal patrol]

I've seen part of a classmates solution, apparently he said something about due to it being discontinous we need to take the limit from both the positive and negative direction of 0

and add them together over 2

[sweet shard]

yea do that

[mortal patrol]

But I don't understand really why? if so is there a theorem for it?

[thick lily]

https://en.wikipedia.org/wiki/Dirichlet–Jordan_test

[thick lily]

so yeah, they definitely messed up in defining f there

but the series is good enough to define if we just assume what they probably meant to put like < there instead

[mortal patrol]

The reason I'm confused is which part I'm supposed to consider? it's a split function

So at f(0)

is it 0 or is it 2?

since it says at t = 0 then it is 0

but between 0 and 2, it is 2

[thick lily]

the fourier series itself doesn't care

[mortal patrol]

What do you mean?

[thick lily]

it just converges to the average of the left and right hand limits to that discontinuity

[mortal patrol]

Ya, but what is f(0)

0 or 2?

[thick lily]

there are really two fs here

[mortal patrol]

That is the confusing part

do you think they messed up with the definition?

[thick lily]

one is the piecewise thing they defined (incorrectly at t=0) and then the other is the series

these aren't the same thing really

kind of like how 1/(1-x) and 1+x+x^2+... are not the same, they don't converge at the same points

[mortal patrol]

hmm okay

I mean the solution I saw, they said (2+2)/2

[thick lily]

the piecewise function probably should have been defined to have 0<t<=2

[mortal patrol]

I assume they then assume that f(0) = 2

[thick lily]

wait do you mean (0+2)/2 ?

[mortal patrol]

This is what they did

[thick lily]

since the left side is 0 and the right side is 2

that left hand limit is wrong, you agree with that?

[mortal patrol]

hmm it's approaching from negative

so it should be 0?

but if it is approaching from positive it should be 2

okay I think it's beginning to make sense to why they defined it wrong, should've been 0<t<=2

I should email the teacher and ask about it

But I mean, since it is defined as 0<=t<=2

[thick lily]

yeah yeah exactly

[mortal patrol]

Isn't it 2+2?

I would assume that it should be 0, if we used the definition you said

[thick lily]

if you draw a graph it should be more apparent

[mortal patrol]

Stealing my classmate's graph

[thick lily]

well it's periodic so that section 2<=t<=pi is where it's 0 should be on the left

no that's a different graph

[mortal patrol]

hmm, let me graph it on desmos real fast

[thick lily]

this is basically what it's gonna look like

[mortal patrol]

hmm okay

So you're stating that approaching from negative direction

it should be 0

looking at the graph, the evidence is strong that it is true yea

[thick lily]

yeah

[mortal patrol]

hmm

I'll email the teacher

Thanks for the help

But would it be the same even if it's continious on t=2?

[sweet shard]

i don't get it, why are you asking if you know the whole solution

[mortal patrol]

I am avoiding to look at the solution

And I don't know

[thick lily]

maybe I am missing something

[mortal patrol]

if it is right even

[sweet shard]

you're looking at it anyway

[mortal patrol]

it's just a classmate's solution

[sweet shard]

oh i see

[mortal patrol]

So I don't want to tunnel vision using his solution

Cuz I've found faults in it

[thick lily]

I missed the part where you said it's an even function

[sweet shard]

yea i thought you meant your teacher's solutions

[mortal patrol]

Does that change it?

[thick lily]

yeah I was assuming the function had a period of pi

and we were repeating this section every pi

[mortal patrol]

2pi

is the period

[sweet shard]

is this your work or your classmates'?

[thick lily]

but if it's even and they're saying it reflects across the y axis and this is the 2pi piece that's repeated, then this is correct

[mortal patrol]

This was in the assignment

[sweet shard]

i assumed it was right since you didn't ask about it

[mortal patrol]

No no, that is right

that was taken from the assignment

[thick lily]

there are no discontinuities at all

[sweet shard]

it'd be better next time to just show the entire given assignment

related to the problem

[mortal patrol]

I can, but it is in swedish

[sweet shard]

doesn't matter

[thick lily]

is this 100% clear why this is now

[sweet shard]

Mero was right

[mortal patrol]

But how is it not discontinous?

[sweet shard]

so you just typed the assignment wrong?

[mortal patrol]

wait

ops

[thick lily]

well once you know it's that reflected piece then it's just a bunch of triangles

[sweet shard]

this is doubly true now

[mortal patrol]

I just flopped hard💀

[thick lily]

here look at this:

https://www.desmos.com/calculator/brnyg4ngsx

[thick lily]

just graphing the first 10 terms of the fourier series you gave lines up, now that we know it's supposed to be even of period 2pi, then this picture I drew is wrong cause it missed that extra info

[mortal patrol]

Makes sense yes

But is there still not some discontinouty? even if it's 2pi period?

should still be some hard cut in the middle

[thick lily]

where

[mortal patrol]

Wait

[thick lily]

the derivative is not continuous (or defined at every mulitple of 2pi)

but the function itself is continuous

[mortal patrol]

So that's its shape?

so why do we use that theorom? of (2+2)/2, I thought that is only used when we find the function to be discontinous or maybe I misunderstood why we use that theorom?

[thick lily]

well it's true when it's continuous as well

it's really more of an added benefit that it gets you the value when it's discontinuous too

[sweet shard]

is it at t=0?

and every 2pi n

[mortal patrol]

no but it must be discontinous at t=0

because it jumps straight from 0 to 2 there and then it's -t + 2

[thick lily]

lol looking at it now I don' tknow what I was saying, I got mixed up at some point

trying to multitask my bad

[mortal patrol]

okay so let's repeat the same question, after I cleared up that I had copied my teacher's assignment wrong

if we approach the limit from negative direction of 0

do we get 0 or 2?😭

[sweet shard]

you have to use this to find f(0)

[mortal patrol]

Yea that's when we do this

That my classmate did

But is it really 2? for t-0 from negative direction

Shouldn't it be 0?

and from the positive direction it approaches 2

[topaz sinew]

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[patent quest]

Linear algebra question

Hey so I have really problems understanding the change the basis/coordinates in linear algebra. So I have this slide. Can someone help me with understanding this with maybe some example?

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[neat mist]

For question 3, why would there be no zeroes?

[whole geode]

There should be one zero for 3. If I'm understanding the graph correctly

[neat mist]

would it be (5,0)?

[trim sable]

Yea but I think there are 2 zeroes

one on the right of the asymptote and one on the left of the asymptote

[whole geode]

Oh I am dumb I missed the left of the graph entirely

[topaz sinew]

@neat mist Has your question been resolved?

[neat mist]

in my teachers answer key she puts "no zeroes"

idk how she got to that

[snow basalt]

she's wrong then lol

as draw, the relation has two zeroes

[trim sable]

👍

[neat mist]

wait so how would i algebraically find the zero on the left?

[trim sable]

well

the graph isn't a function

[snow basalt]

you dont have equations, so you can do it algebraically

[trim sable]

Idk the rules entirely about that but it might not have zeroes if it's not a function

technically speaking

[neat mist]

oh wait

[snow basalt]

your best bet would be to look that its somewhere between -2 and -4 and guess something like -2.5

[neat mist]

maybe she put no zeroes because the graph isnt a function?

[trim sable]

I think so

[snow basalt]

surely a sensible definition of "zero" for relations would just be places where the relation intersects the y-axis

doesn't need to be changed from the way its defined for functions

[trim sable]

Google AI says otherwise

but it's AI so

[snow basalt]

ok?

google ai omegalul

[winter egret]

If the relation is not a function then the concepts of functions don't apply. The graph in diagram 3 does not form a valid function

[neat mist]

so because it isnt a function, there would not be any zeroes?

[winter egret]

I think your teacher is doing something very nonstandard here because they're asking for the domain, range and zeros of a relation but those concepts don't typically make much sense for any arbitrary relation

[snow basalt]

idk

[neat mist]

shes a terrible teacher so im not suprised

[snow basalt]

when i was first taught the concept of a relation they defined said terms

but could be different

not zeroes admittedly

[winter egret]

Sorry, the domain and range of a relation are well-defined and standard concepts

but the zero probably is not

[snow basalt]

i think this is a very silly question if the answer is "there are no zeroes since its not a function" when the definition of a zero extends so obviously to arbitrary relations but i guess so

[trail meteor]

bro is cooked

[winter egret]

I think it's an okay question because it forces the student to think about whether zeros do extend to arbitrary relations or not

and funnily enough I don't see at all why you would define such a concept

or actually

I don't see how you could

because even at best you could only define it for subsets of A x B where B contains some zero element

[snow basalt]

Would not a zero in a relation be an element (0,x) in the relation?

[winter egret]

but there's no guarantee that that would be the case in general

[snow basalt]

but we're looking specifically at relations on R here

the definition of zero for a function makes just as little sense if you dont take the function to be on R

[winter egret]

With functions it's very standard that the codomain is some "numeric" set

With relations, not so much

[snow basalt]

like {(a,c) (b,d)} qualifies as a function on the alphabet, but certainly there's no sensible notion of a zero

idk, for me there's not a difference enough to think this is some useful distinction

[winter egret]

but you're right that the zero of a function doesn't make sense for any general completely arbitrary function

I mean, the zero of a function is a useful concept for obvious reasons

because it allows you to standardize the procedure of solving polynomial equations for example

But there generally just is no need for a super niche concept that would only apply for all relations over R

Because for those relations that are functions, well you have the zero of a function

[topaz sinew]

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[winter egret]

and for those relations that are not functions, whether or not one of the elements is 0 is not usually so interesting that the concept should warrant its own terminology

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[winter egret]

.So maybe in some sense -1 is a "zero" of <= because -1<=0 but how is that special at all, I don't know

[snow basalt]

but its not its own terminology, and despite the fact its not something you'll talk about a lot, there's no reason not to just have the exact same definition extend more generally for zero effort, it certainly holds nonzero utility! but this is more of a philosophical thing now lol

[winter egret]

I think it holds negative utility because teaching something that no mathematician would ever need or use is a waste of everyone's time

[snow basalt]

I guess so

But in the context of the question i still think asking the question is not right, i.e. "there are no zeroes" would be a sensible expected answer to a question where zeroes was a concept that doesn't make sense, rather than one where it just doesnt hold usefulness

[winter egret]

A definition (of this kind) is itself not math and thus a definition (of this kind) should only be taught if it helps you to reason about mathematical objects

[snow basalt]

True

[winter egret]

Well it doesn't make sense if no one's defined what it means

[snow basalt]

in the context of being surrounded by three functions, I don't think its fair to say it doesn't make sense. It doesn't fit exactly to a definition, but that's purely because we are working on a superset of something where it does work. I think to say this is a sensible question is bad pedagogy, if I see "find the x of y", but I only know how to find the "x of z", I'm gonna look back for where we defined the "x of y" in class, and go ask the professor if something specific is the definition failing that, and maybe try to extend the x of z to x of y - the language of the question has some degree of implication that "the zeroes of relation R" is a concept that makes sense imo.

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[undone sluice]

how do you find the least possible multiplicity of a root/zero by just looking at the graph of the polynomial

[wary tulip]

!original

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[undone sluice]

Answer the following questions about p(x).
(a) What are the end behaviours of p(x).
(b) How many turning points does p(x) have?
(c) What is the least possible degree of p(x)?
(d) Write down the roots of p(x) and their least possible multiplicities.
(e) Use the roots and the y-intercept of p(x) to write down a possible equation
for p(x).

I'm confused about question d

would it just be multiplicty of 1 for all the roots except 4 which would be 2?

[wary tulip]

probably

[undone sluice]

is my math teacher just funky 😭

can't find any answers on the internet

[wary tulip]

this matches and you can't reduce the multiplicity on any of them

[undone sluice]

Thank you so much

been stuck on this forever and had no clue what the graph equation even looked like

[wary tulip]

well you need a factor of (x+5) to have a root at -5 etc

[undone sluice]

why does it have 112 at the bottom?

just to make it fit on the screen?

[wary tulip]

just experimenting until it matches

[undone sluice]

ahh, makes sense

once again thank you

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[tacit turret]

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[tacit turret]

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